Fully Nonlocal Functionals Along the Adiabatic Connection of Density Functional Theory

Inspired by the exact form of the strongly interacting limit of density functional theory, Vuckovic and Gori Giorgi have recently proposed [J. Phys. Chem. Lett. 2017, 8, 2799] the multiple radii functional (MRF), a new framework for the construction of exchange-correlation (xc) energy approximations able to describe strong correlation electronic effects. To facilitate the construction of improved approximations based on the MRF functional, in the present work we use reverse engineering strategies to reveal the forms of the MRF functional which reproduce the exact xc functional for small atoms. We also develop a procedure that allows the MRF functional to be built on the top of exact exchange. Using the adiabatic connection representation of the xc functional, we also investigate routes for the construction of the correlation functional by combining information from the physical, weakly and strongly interacting regimes. We highlight the advantages of this approach over previous adiabatic connection-based approaches for the treatment of strong correlation and discuss how it can be used for recovering the presently missing kinetic component of the correlation energy in the MRF framework.